Trump, who is in NY for the U.N. General Assembly, told reporters he would meet with Rosenstein on Thursday when he returns to Washington.

This is a breaking news and developing story.

The Rosenstein furore came just six weeks ahead of the November 6 congressional elections, and his removal could become an explosive political issue as Trump's fellow Republicans try to keep control of Congress.

The development follows a report that America's second most senior law official previous year talked about ousting Mr Trump and secretly recording him.

Republican politicos have been urging Trump not to fire Rosenstein until after the midterm elections, arguing that doing so would cause even more headache for the party struggling to hang on to the House and possibly the Senate.

Rosenstein denied the report.

Trump is well-known as a large coward who can't fire people in person, and he is a creature who can only understand the human experience through major media, so this looks like a full-court PR press to pressure Rosenstein into resigning, so Trump can appoint a stooge to oversee the Mueller investigation.

Rosenstein is the official who started the special counsel investigation into Russian contacts with Donald Trump's team after Attorney General Jeff Sessions had recused himself from the matter.

Rosenstein visited the White House on Monday and met with Chief of Staff John Kelly with the expectation that he would be fired, sources told ABC News, but he remained in the post as of Monday afternoon. At a Missouri rally last Friday, Trump said there was a "lingering stench" at the Department of Justice and that he was going to get rid of it.

The Associated Press also reported that Rosenstein was expected to be fired on Monday.

Others involved in those May 2017 discussions said Rosenstein's comments about secretly recording the president were sarcastic, and came as McCabe was pressing the Justice Department to open an investigation into the president over the firing of Comey as possible obstruction of justice. He plans to step down, Axios reported. Trump has repeatedly attacked Sessions for that move.

Trump has repeatedly dismissed the Mueller probe as a "witch hunt" created to delegitimize his election victory and undermine his presidency.

As deputy attorney general, Rosenstein has made two public announcements of indictments brought by the special counsel - one against Russians accused of hacking into Democratic email accounts, the other against Russians accused of running a social media troll farm to sway public opinion.

"There is nothing more important to the integrity of law enforcement and the rule of law than protecting the investigation of Special Counsel (Robert) Mueller", McCabe said in a statement.